The current in a coil varies with time \(t\) as \(I= 3 t^{2} +2t\). If the inductance of coil be \(10\) mH, the value of induced emf at \(t=2~\text{s}\) will be:
1. \(0.14~\text{V}\)
2. \(0.12~\text{V}\)
3. \(0.11~\text{V}\)
4. \(0.13~\text{V}\)

The network shown in figure is a part of a complete circuit. If at a certain instant, the current \(i\) is \(10\) A and is increasing at the rate of \(4\times 10^{3}\) A/sec, then \(V_A-V_B\) is:

A rod \(AB\) of length \(l\) is moving with constant speed \(v\) in a uniform magnetic field on a conducting \(U\)-shaped wire as shown. If the rate of loss of heat energy across resistance \(R\) is \(Q,\) then the force needed parallel to velocity to keep rod moving with constant speed \(v\) is:

1. \(Qv\)

2. \(\dfrac{Q}{v}\)

3. \(\dfrac{Q^2}{v}\)

4. \(Q^2v\)

An electric potential difference will be induced between the ends of the conductor shown in the diagram when the conductor moves in the direction of:

1. \(P\)
2. \(Q\)
3. \(L\)
4. \(M\)

In a circuit with a coil of resistance \(2\) ohms, the magnetic flux changes from \(2.0\) Wb to \(10.0\) Wb in \(0.2\) second. The charge that flows in the coil during this time is:
1. \(5.0\) coulomb
2. \(4.0\) coulomb
3. \(1.0\) coulomb
4. \(0.8\) coulomb

A long solenoid of diameter \(0.1\) m has \(2\times 10^{4}\) turns per meter. At the centre of the solenoid, a coil of \(100\) turns and a radius of \(0.01\) m is placed with its axis coinciding with the solenoid's axis.  The current in the solenoid reduces at a constant rate from \(0\) A to \(4\) A in \(0.05\) s. If the resistance of the coil is \(10\pi^2~\Omega\), the total charge flowing through the coil during this time is:
1. \(32\pi~\mu\text{C}\)
2. \(16~\mu\text{C}\)
3. \(32~\mu\text{C}\)
4. \(16\pi~\mu\text{C}\)

A conducting square frame of side \(a\) and a long straight wire carrying current \(i\) are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity \(v\). The emf induced in the frame will be proportional to:
                
1. \(\frac{1}{x^2}\)
2. \(\frac{1}{(2x-a)^2}\)
3. \(\frac{1}{(2x+a)^2}\)
4. \(\frac{1}{(2x-a)\times (2x+a)}\)